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1% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
2%!TEX root = Vorbis_I_spec.tex
3\section{Floor type 1 setup and decode} \label{vorbis:spec:floor1}
4
5\subsection{Overview}
6
7Vorbis floor type one uses a piecewise straight-line representation to
8encode a spectral envelope curve. The representation plots this curve
9mechanically on a linear frequency axis and a logarithmic (dB)
10amplitude axis. The integer plotting algorithm used is similar to
11Bresenham's algorithm.
12
13
14
15\subsection{Floor 1 format}
16
17\subsubsection{model}
18
19Floor type one represents a spectral curve as a series of
20line segments. Synthesis constructs a floor curve using iterative
21prediction in a process roughly equivalent to the following simplified
22description:
23
24\begin{itemize}
25 \item the first line segment (base case) is a logical line spanning
26from x_0,y_0 to x_1,y_1 where in the base case x_0=0 and x_1=[n], the
27full range of the spectral floor to be computed.
28
29\item the induction step chooses a point x_new within an existing
30logical line segment and produces a y_new value at that point computed
31from the existing line's y value at x_new (as plotted by the line) and
32a difference value decoded from the bitstream packet.
33
34\item floor computation produces two new line segments, one running from
35x_0,y_0 to x_new,y_new and from x_new,y_new to x_1,y_1. This step is
36performed logically even if y_new represents no change to the
37amplitude value at x_new so that later refinement is additionally
38bounded at x_new.
39
40\item the induction step repeats, using a list of x values specified in
41the codec setup header at floor 1 initialization time. Computation
42is completed at the end of the x value list.
43
44\end{itemize}
45
46
47Consider the following example, with values chosen for ease of
48understanding rather than representing typical configuration:
49
50For the below example, we assume a floor setup with an [n] of 128.
51The list of selected X values in increasing order is
520,16,32,48,64,80,96,112 and 128. In list order, the values interleave
53as 0, 128, 64, 32, 96, 16, 48, 80 and 112. The corresponding
54list-order Y values as decoded from an example packet are 110, 20, -5,
55-45, 0, -25, -10, 30 and -10. We compute the floor in the following
56way, beginning with the first line:
57
58\begin{center}
59\includegraphics[width=8cm]{floor1-1}
60\captionof{figure}{graph of example floor}
61\end{center}
62
63We now draw new logical lines to reflect the correction to new_Y, and
64iterate for X positions 32 and 96:
65
66\begin{center}
67\includegraphics[width=8cm]{floor1-2}
68\captionof{figure}{graph of example floor}
69\end{center}
70
71Although the new Y value at X position 96 is unchanged, it is still
72used later as an endpoint for further refinement. From here on, the
73pattern should be clear; we complete the floor computation as follows:
74
75\begin{center}
76\includegraphics[width=8cm]{floor1-3}
77\captionof{figure}{graph of example floor}
78\end{center}
79
80\begin{center}
81\includegraphics[width=8cm]{floor1-4}
82\captionof{figure}{graph of example floor}
83\end{center}
84
85A more efficient algorithm with carefully defined integer rounding
86behavior is used for actual decode, as described later. The actual
87algorithm splits Y value computation and line plotting into two steps
88with modifications to the above algorithm to eliminate noise
89accumulation through integer roundoff/truncation.
90
91
92
93\subsubsection{header decode}
94
95A list of floor X values is stored in the packet header in interleaved
96format (used in list order during packet decode and synthesis). This
97list is split into partitions, and each partition is assigned to a
98partition class. X positions 0 and [n] are implicit and do not belong
99to an explicit partition or partition class.
100
101A partition class consists of a representation vector width (the
102number of Y values which the partition class encodes at once), a
103'subclass' value representing the number of alternate entropy books
104the partition class may use in representing Y values, the list of
105[subclass] books and a master book used to encode which alternate
106books were chosen for representation in a given packet. The
107master/subclass mechanism is meant to be used as a flexible
108representation cascade while still using codebooks only in a scalar
109context.
110
111\begin{Verbatim}[commandchars=\\\{\}]
112
113 1) [floor1\_partitions] = read 5 bits as unsigned integer
114 2) [maximum\_class] = -1
115 3) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{
116
117 4) vector [floor1\_partition\_class\_list] element [i] = read 4 bits as unsigned integer
118
119 \}
120
121 5) [maximum\_class] = largest integer scalar value in vector [floor1\_partition\_class\_list]
122 6) iterate [i] over the range 0 ... [maximum\_class] \{
123
124 7) vector [floor1\_class\_dimensions] element [i] = read 3 bits as unsigned integer and add 1
125 8) vector [floor1\_class\_subclasses] element [i] = read 2 bits as unsigned integer
126 9) if ( vector [floor1\_class\_subclasses] element [i] is nonzero ) \{
127
128 10) vector [floor1\_class\_masterbooks] element [i] = read 8 bits as unsigned integer
129
130 \}
131
132 11) iterate [j] over the range 0 ... (2 exponent [floor1\_class\_subclasses] element [i]) - 1 \{
133
134 12) array [floor1\_subclass\_books] element [i],[j] =
135 read 8 bits as unsigned integer and subtract one
136 \}
137 \}
138
139 13) [floor1\_multiplier] = read 2 bits as unsigned integer and add one
140 14) [rangebits] = read 4 bits as unsigned integer
141 15) vector [floor1\_X\_list] element [0] = 0
142 16) vector [floor1\_X\_list] element [1] = 2 exponent [rangebits];
143 17) [floor1\_values] = 2
144 18) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{
145
146 19) [current\_class\_number] = vector [floor1\_partition\_class\_list] element [i]
147 20) iterate [j] over the range 0 ... ([floor1\_class\_dimensions] element [current\_class\_number])-1 \{
148 21) vector [floor1\_X\_list] element ([floor1\_values]) =
149 read [rangebits] bits as unsigned integer
150 22) increment [floor1\_values] by one
151 \}
152 \}
153
154 23) done
155\end{Verbatim}
156
157An end-of-packet condition while reading any aspect of a floor 1
158configuration during setup renders a stream undecodable. In addition,
159a \varname{[floor1\_class\_masterbooks]} or
160\varname{[floor1\_subclass\_books]} scalar element greater than the
161highest numbered codebook configured in this stream is an error
162condition that renders the stream undecodable. Vector
163[floor1\_x\_list] is limited to a maximum length of 65 elements; a
164setup indicating more than 65 total elements (including elements 0 and
1651 set prior to the read loop) renders the stream undecodable. All
166vector [floor1\_x\_list] element values must be unique within the
167vector; a non-unique value renders the stream undecodable.
168
169\subsubsection{packet decode} \label{vorbis:spec:floor1-decode}
170
171Packet decode begins by checking the \varname{[nonzero]} flag:
172
173\begin{Verbatim}[commandchars=\\\{\}]
174 1) [nonzero] = read 1 bit as boolean
175\end{Verbatim}
176
177If \varname{[nonzero]} is unset, that indicates this channel contained
178no audio energy in this frame. Decode immediately returns a status
179indicating this floor curve (and thus this channel) is unused this
180frame. (A return status of 'unused' is different from decoding a
181floor that has all points set to minimum representation amplitude,
182which happens to be approximately -140dB).
183
184
185Assuming \varname{[nonzero]} is set, decode proceeds as follows:
186
187\begin{Verbatim}[commandchars=\\\{\}]
188 1) [range] = vector \{ 256, 128, 86, 64 \} element ([floor1\_multiplier]-1)
189 2) vector [floor1\_Y] element [0] = read \link{vorbis:spec:ilog}{ilog}([range]-1) bits as unsigned integer
190 3) vector [floor1\_Y] element [1] = read \link{vorbis:spec:ilog}{ilog}([range]-1) bits as unsigned integer
191 4) [offset] = 2;
192 5) iterate [i] over the range 0 ... [floor1\_partitions]-1 \{
193
194 6) [class] = vector [floor1\_partition\_class] element [i]
195 7) [cdim] = vector [floor1\_class\_dimensions] element [class]
196 8) [cbits] = vector [floor1\_class\_subclasses] element [class]
197 9) [csub] = (2 exponent [cbits])-1
198 10) [cval] = 0
199 11) if ( [cbits] is greater than zero ) \{
200
201 12) [cval] = read from packet using codebook number
202 (vector [floor1\_class\_masterbooks] element [class]) in scalar context
203 \}
204
205 13) iterate [j] over the range 0 ... [cdim]-1 \{
206
207 14) [book] = array [floor1\_subclass\_books] element [class],([cval] bitwise AND [csub])
208 15) [cval] = [cval] right shifted [cbits] bits
209 16) if ( [book] is not less than zero ) \{
210
211 17) vector [floor1\_Y] element ([j]+[offset]) = read from packet using codebook
212 [book] in scalar context
213
214 \} else [book] is less than zero \{
215
216 18) vector [floor1\_Y] element ([j]+[offset]) = 0
217
218 \}
219 \}
220
221 19) [offset] = [offset] + [cdim]
222
223 \}
224
225 20) done
226\end{Verbatim}
227
228An end-of-packet condition during curve decode should be considered a
229nominal occurrence; if end-of-packet is reached during any read
230operation above, floor decode is to return 'unused' status as if the
231\varname{[nonzero]} flag had been unset at the beginning of decode.
232
233
234Vector \varname{[floor1\_Y]} contains the values from packet decode
235needed for floor 1 synthesis.
236
237
238
239\subsubsection{curve computation} \label{vorbis:spec:floor1-synth}
240
241Curve computation is split into two logical steps; the first step
242derives final Y amplitude values from the encoded, wrapped difference
243values taken from the bitstream. The second step plots the curve
244lines. Also, although zero-difference values are used in the
245iterative prediction to find final Y values, these points are
246conditionally skipped during final line computation in step two.
247Skipping zero-difference values allows a smoother line fit.
248
249Although some aspects of the below algorithm look like inconsequential
250optimizations, implementors are warned to follow the details closely.
251Deviation from implementing a strictly equivalent algorithm can result
252in serious decoding errors.
253
254{\em Additional note:} Although \varname{[floor1\_final\_Y]} values in
255the prediction loop and at the end of step 1 are inherently limited by
256the prediction algorithm to [0, \varname{[range]}), it is possible to
257 abuse the setup and codebook machinery to produce negative or
258 over-range results. We suggest that decoder implementations guard
259 the values in vector \varname{[floor1\_final\_Y]} by clamping each
260 element to [0, \varname{[range]}) after step 1. Variants of this
261 suggestion are acceptable as valid floor1 setups cannot produce
262 out of range values.
263
264\begin{description}
265\item[step 1: amplitude value synthesis]
266
267Unwrap the always-positive-or-zero values read from the packet into
268+/- difference values, then apply to line prediction.
269
270\begin{Verbatim}[commandchars=\\\{\}]
271 1) [range] = vector \{ 256, 128, 86, 64 \} element ([floor1\_multiplier]-1)
272 2) vector [floor1\_step2\_flag] element [0] = set
273 3) vector [floor1\_step2\_flag] element [1] = set
274 4) vector [floor1\_final\_Y] element [0] = vector [floor1\_Y] element [0]
275 5) vector [floor1\_final\_Y] element [1] = vector [floor1\_Y] element [1]
276 6) iterate [i] over the range 2 ... [floor1\_values]-1 \{
277
278 7) [low\_neighbor\_offset] = \link{vorbis:spec:low:neighbor}{low\_neighbor}([floor1\_X\_list],[i])
279 8) [high\_neighbor\_offset] = \link{vorbis:spec:high:neighbor}{high\_neighbor}([floor1\_X\_list],[i])
280
281 9) [predicted] = \link{vorbis:spec:render:point}{render\_point}( vector [floor1\_X\_list] element [low\_neighbor\_offset],
282 vector [floor1\_final\_Y] element [low\_neighbor\_offset],
283 vector [floor1\_X\_list] element [high\_neighbor\_offset],
284 vector [floor1\_final\_Y] element [high\_neighbor\_offset],
285 vector [floor1\_X\_list] element [i] )
286
287 10) [val] = vector [floor1\_Y] element [i]
288 11) [highroom] = [range] - [predicted]
289 12) [lowroom] = [predicted]
290 13) if ( [highroom] is less than [lowroom] ) \{
291
292 14) [room] = [highroom] * 2
293
294 \} else [highroom] is not less than [lowroom] \{
295
296 15) [room] = [lowroom] * 2
297
298 \}
299
300 16) if ( [val] is nonzero ) \{
301
302 17) vector [floor1\_step2\_flag] element [low\_neighbor\_offset] = set
303 18) vector [floor1\_step2\_flag] element [high\_neighbor\_offset] = set
304 19) vector [floor1\_step2\_flag] element [i] = set
305 20) if ( [val] is greater than or equal to [room] ) \{
306
307 21) if ( [highroom] is greater than [lowroom] ) \{
308
309 22) vector [floor1\_final\_Y] element [i] = [val] - [lowroom] + [predicted]
310
311 \} else [highroom] is not greater than [lowroom] \{
312
313 23) vector [floor1\_final\_Y] element [i] = [predicted] - [val] + [highroom] - 1
314
315 \}
316
317 \} else [val] is less than [room] \{
318
319 24) if ([val] is odd) \{
320
321 25) vector [floor1\_final\_Y] element [i] =
322 [predicted] - (([val] + 1) divided by 2 using integer division)
323
324 \} else [val] is even \{
325
326 26) vector [floor1\_final\_Y] element [i] =
327 [predicted] + ([val] / 2 using integer division)
328
329 \}
330
331 \}
332
333 \} else [val] is zero \{
334
335 27) vector [floor1\_step2\_flag] element [i] = unset
336 28) vector [floor1\_final\_Y] element [i] = [predicted]
337
338 \}
339
340 \}
341
342 29) done
343
344\end{Verbatim}
345
346
347
348\item[step 2: curve synthesis]
349
350Curve synthesis generates a return vector \varname{[floor]} of length
351\varname{[n]} (where \varname{[n]} is provided by the decode process
352calling to floor decode). Floor 1 curve synthesis makes use of the
353\varname{[floor1\_X\_list]}, \varname{[floor1\_final\_Y]} and
354\varname{[floor1\_step2\_flag]} vectors, as well as [floor1\_multiplier]
355and [floor1\_values] values.
356
357Decode begins by sorting the scalars from vectors
358\varname{[floor1\_X\_list]}, \varname{[floor1\_final\_Y]} and
359\varname{[floor1\_step2\_flag]} together into new vectors
360\varname{[floor1\_X\_list]'}, \varname{[floor1\_final\_Y]'} and
361\varname{[floor1\_step2\_flag]'} according to ascending sort order of the
362values in \varname{[floor1\_X\_list]}. That is, sort the values of
363\varname{[floor1\_X\_list]} and then apply the same permutation to
364elements of the other two vectors so that the X, Y and step2\_flag
365values still match.
366
367Then compute the final curve in one pass:
368
369\begin{Verbatim}[commandchars=\\\{\}]
370 1) [hx] = 0
371 2) [lx] = 0
372 3) [ly] = vector [floor1\_final\_Y]' element [0] * [floor1\_multiplier]
373 4) iterate [i] over the range 1 ... [floor1\_values]-1 \{
374
375 5) if ( [floor1\_step2\_flag]' element [i] is set ) \{
376
377 6) [hy] = [floor1\_final\_Y]' element [i] * [floor1\_multiplier]
378 7) [hx] = [floor1\_X\_list]' element [i]
379 8) \link{vorbis:spec:render:line}{render\_line}( [lx], [ly], [hx], [hy], [floor] )
380 9) [lx] = [hx]
381 10) [ly] = [hy]
382 \}
383 \}
384
385 11) if ( [hx] is less than [n] ) \{
386
387 12) \link{vorbis:spec:render:line}{render\_line}( [hx], [hy], [n], [hy], [floor] )
388
389 \}
390
391 13) if ( [hx] is greater than [n] ) \{
392
393 14) truncate vector [floor] to [n] elements
394
395 \}
396
397 15) for each scalar in vector [floor], perform a lookup substitution using
398 the scalar value from [floor] as an offset into the vector \link{vorbis:spec:floor1:inverse:dB:table}{[floor1\_inverse\_dB\_static\_table]}
399
400 16) done
401
402\end{Verbatim}
403
404\end{description}
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